By Meghan Eisold

Recently, concussions have been a major concern among soccer players. When I was in high-school, some girls wore protective head gear, pictured below, to prevent concussions. I decided to determine whether the headgear can significantly lower the force that the ball exerts on a soccer player while heading the ball.

 

Mass of Soccer ball: 0.43 kg

Mass of soccer player’s: 75 kg

Horizontal Velocity of a kicked soccer ball(v₁): 70 km/h (19.44 m/s)

I assumed that the Vertical Velocity of the ball is negligible 

Horizontal velocity of soccer player (v2): -5 km/h (-1.39 m/s) (negative=direction soccer player is traveling)

Vertical Velocity of Soccer Player is assumed to be 0 (player is not jumping)

First I determined the velocity of the ball and the player after the collision:

Elastic collisions

Equation 1: m₁v₁ + m₂v₂ = m₁v₁^’ +m₂v₂^’

(0.43 kg)(19.44 m/s)+(75 kg)(-1.39 m/s)=(0.43 kg)v₁^’ +(75 kg)v₂^’

Equation 2: v₁+v₁^’ = v₂ + v₂^’

(19.44 m/s) +v₁^’ = (0.43 kg) + v₂^’

v₁^’= v₂^’ – 19.01

Combine equations: (0.43 kg)(19.44 m/s)+(75 kg)(-1.39 m/s)=(0.43 kg)(v₂^’ – 19.01

m/s) +(75 kg)v₂’

-95.89= -8.1743 +0.43v₂^’+(75 kg)v₂’            v₂^’=-1.16 m/s

(19.44 m/s) +v₁^’ = (1.39 m/s) + (1.60 m/s)    v₁^’=-19.21 m/s

I then used the final velocities to determine the force that the ball would exert on the player during the appropriate collision time. I estimated that the headgear would extend the collision time by 5 ms.

Collision without headgear: t=25 ms =0.0025s

∑FΔ t = Δ p  

∑F_{b on p}(0.0025s)=(75 kg)(-1.16 m/s)-( 75 kg)(-1.39 m/s)

∑F_{b on p}=6900 N

Collision with Collision with headgear: t=30 ms =0.0030s

∑FΔ t = Δ p  

∑F_{b on p}(0.0030s)=(75 kg)(-1.16 m/s)-( 75 kg)(-1.39 m/s)

∑F_{b on p}=5750 N

From these results I can conclude that the headgear does lower the force that is exerted on the player, but it is not a significant difference.